The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become $…….\,hours$

The planet Mars has two moons, phobos and delmos.

$(i)$ phobos has a period $7$ hours, $39$ minutes and an orbital radius of $9.4 \times 10^{3} \;km .$ Calculate the mass of mars.

$(ii)$ Assume that earth and mars move in circular orbits around the sun. with the martian orbit being $1.52$ times the orbital radius of the earth. What is the length of the martian year in days?

Earth is revolving around the sun if the distance of the Earth from the Sun is reduced to $\frac{1}{4}^{th}$ of the present distance then the present day length reduced by

The mean radius of the earth's orbit round the sun is $1.5 \times 10^{11}.$ The mean radius of the orbit of mercury round the sun is $6 \times10^{10}\,m.$ The mercury will rotate around the sun in

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.

$Assertion$ $(A)$ : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.

$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.

In the light of the above statements, choose the most appropriate answer from the options given below: